Single-variable formulations and isogeometric discretizations for shear deformable beams

被引：100
作者：
Kiendl, J. [1 ]
Auricchio, F. [1 ,2 ]
Hughes, T. J. R. [3 ]
Reali, A. [1 ,2 ]
机构：
[1] Univ Pavia, Dept Civil Engn & Architecture, I-27100 Pavia, Italy
[2] IMATI CNR, Pavia, Italy
[3] Univ Texas Austin, Inst Computat Engn & Sci, Austin, TX 78712 USA
来源：
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2015年 / 284卷
基金：
欧洲研究理事会; 美国国家科学基金会;
关键词：
Timoshenko beam; Shear-deformable; Locking-free; Isogeometric; Collocation; Finite elements; COLLOCATION METHODS; FINITE-ELEMENTS; TIMOSHENKO; VIBRATIONS; LOCKING; NURBS; RODS;
D O I：
10.1016/j.cma.2014.11.011
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
We present numerical formulations of Timoshenko beams with only one unknown, the bending displacement, and it is shown that all variables of the beam problem can be expressed in terms of it and its derivatives. We develop strong and weak forms of the problem. The strong form of the problem involves the fourth derivative of the bending displacement, whereas the symmetric weak form involves, somewhat surprisingly, third and second derivatives. Based on these, we develop isogeometric collocation and Galerkin formulations, that are completely locking-free and involve only half the degrees of freedom compared to standard Timoshenko beam formulations. Several numerical tests are presented to demonstrate the performance of the proposed formulations. (C) 2014 Elsevier B.V. All rights reserved.
引用
收藏
页码：988 / 1004
页数：17
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